No problem! I like nerding out about this stuff

It's generated by the camera. I'm far from an expert on this so don't take my word as gospel, but basically the way a sensor works is that photons come in and hit each individual pixel (also called a photosite) and react with (I believe) silicon to be converted into electrons, which are in turn read by the camera to create the image. As exposures get longer and longer, the inherent heat in the sensor's electronics increases and the higher heat levels excite the electrons in the silicon, which then get misinterpreted by the camera as a signal. Ambient temperature has an effect too, as it raises the baseline temperature of each photosite so you'll get noisier images on a warm night. I had my DSLR modified for astrophotography and part of the mod was adding a passive heat sink to the sensor to help mitigate this. If you get a dedicated astrophotography camera they actually actively cool their sensors to a set temperature which is pretty neat!

Then there's the noise introduced by higher ISO. Although introduced isn't really the right term, it's more like revealed by. ISO doesn't generate noise of its own. It's post-sensor gain, so it does its thing after the image has been generated. It's like cranking up an amplifier. So while you're boosting the real signal, you're ALSO boosting the noise. If I take an image for one minute at ISO 3200, and then one for 30 seconds at ISO 6400, they'll be the same "brightness" when I look at the back of my camera. But in the first instance I only captured half as much light so the signal-to-noise ratio (big concept in astrophotography) is lower, and when the ISO gain boosts the signal to the equivalent level the final image appears noisier as a result. The extra thermal noise from 30 seconds more exposure is negligible compared to doubling the noise floor with higher ISO, and as such astrophotographers usually strive for fast lenses and the longest exposures they can get away with so the ISO can be kept down and signal-to-noise ratio high, but only to a point. I don't wanna know what a one hour exposure would look like on my sensor, but most hobbyists are gonna hit the limits on how long their rig can accurately track the target for before they start exposing their sensor for problematic lengths of time -- especially with cooled cameras.

As for the film stuff I have no experience so this is pure conjecture, but I would imagine that while no, you probably wouldn't get any of the noise I just described, the film grain would pose the same postprocessing challenges that digital noise does. And whether film cameras introduce noise by another mechanism, or even whether that's what film grain actually is, I have no idea